A gradual increase in membrane resistance is critical to reduced fluctuation-based modulation of input-output responses in an eLlF model

As a result, the changes in firing rate , rheobase and gain induced by membrane voltage fluctuations correspond more closely to those observed in stellate cells when AT is set to 15 mV (Fig 4D and 4E).

Large AT values reduce modulation of input-output responses through voltage fluctuations by slowing membrane voltage

By generating a shallow f- V, a large AT limits the ability for a change in voltage brought about through random fluctuations to increase spike firing rate .

Large AT values reduce modulation of input-output responses through voltage fluctuations by slowing membrane voltage

Conversely, when AT is small and the f-Vrelationship is steep, voltage fluctuations can give rise to a large change in spike firing rate (Fig 7D).

Previous modeling and experimental work has shown that random voltage fluctuations induce the largest increase in firing rate in the low spike rate region of the f-I curve, near the transition between rest and firing [8—10,19,20,24].

For each cell, we measured the change in firing rate brought about by voltage fluctuations for low, mid and high current input regions relative to the same cell’sf-I curve acquired without fluctuations.

Each inhibitory neuron receives stronger inputs from one of the output neuron groups and, as a result, shows a higher firing rate for the corresponding external signal.

Model

The input layer shows rate-modulated Poisson firing based on events at the external layer and external noise, which is approximated with the constant firing rate {no}.

Model

We considered the case for information encoded in the correlated activity of input neurons [34,35], and fixed the average firing rate of all input neurons at the constant value UOX (See Table 1 and 2 for the list of variables and parameters).

Model

If the firing rate of input neuron i is of the neuron qiy, then common inputs from the external layer induce a temporal correlation proportional to

Optimal correlation timescale changes depend on the noise source

To make a clear comparison, in the simulation of random noise, we kept qN = 0 and changed the spontaneous firing rate of the input neurons (no) to modify the noise intensity, whereas in simulation of crosstalk noise we removed random noise (i.e., no 2 0) and changed qN.

STDP and Bayesian ICA

In addition, when information is coded by firing rate , homeostatic plasticity is critically important, because STDP itself does not mimic Bienenstock-Cooper-Munro learning [18].

Here, we used both a reduced firing rate model and numerical simulations of a spiking network model of the striatum to analyze the dynamic balance of spiking activities in D1 and D2 MSNs.

Author Summary

Our analysis and simulations show that the asymmetric connectivity between these neurons gives rise to a decision transition threshold (DTT), as a consequence D1 (D2) neurons have higher firing rate at lower (higher) average cortical firing rates .

D1 MSNs require overall stronger input from cortex than D2 MSNs

These inequalities imply that if the two MSN subpopulations receive the same amount of excitatory input, D2 MSNs will always have a higher firing rate .

D1 MSNs require overall stronger input from cortex than D2 MSNs

In our spiking network simulations this corresponded to a lower mean firing rate of the D1 population compared to the D2 population.

D1 MSNs require overall stronger input from cortex than D2 MSNs

To estimate how much additional excitation would be required for D1 MSNs to have their firing rates exceed over those of D2 MSNs, we systematically varied the drive of cortical inputs to D1 and D2 MSNs and calculated the response firing rates of the two subpopulations, for the firing rate model (Fig 2).

Introduction

Here we describe the effect of the heterogenous connectivity of D1 and D2 neurons on their mutual interactions using both a reduced firing rate model and numerical simulations of a spiking striatal network model.

Introduction

We show that the firing rates of both D1 and D2 MSNs change in a non-monotonic manner in response to cortical input rates and correlations.

Introduction

Correlations in the input can further change the range of cortical inputs for which either D1 or D2 MSNs have the higher firing rate .

Results

Specifically, we evaluated the firing rates of the D1 and D2 MSNs, in response to cortical input rates and input correlations.

We analyzed the effect of factors, such as the mean firing rate and the recording duration, on the detectability of oscillations and their significance, and tested these theoretical results on experimental data recorded in Parkinsonian nonhuman primates.

Introduction

The generation of each spike within the train is assumed to be dependent on an underlying instantaneous firing rate .

Introduction

Thus, despite an underlying oscillatory firing rate , in most cases the neuron will skip a large portion of the oscillation cycle or even entire cycles [11].

Introduction

The most simplistic statistical spike train model assumes that the generation of each spike is dependent solely on the underlying instantaneous firing rate , and is independent of all other previous spikes.

Results

where r0 is the baseline firing rate , 0 g m g 1 is the modulation index, and f0 is the oscillation frequency.

Results

The SNR of these simulated neurons varies linearly as a function of the base firing rate of the neuron (Fig 1H).

Results

As a result, the detection of significant oscillations crossing a specific SNR threshold is not possible for a neuron with a low baseline firing rate (Fig 1E), compared to neurons with higher firing rates (Fig 1F—1G), which have a higher SNR and are therefore identified as oscillatory.

Previous work has demonstrated that both the firing rate of neurons (rate code) and the timing of their stimulus-evoked responses (temporal code) can be used by auditory cortical neurons to represent temporal information.

Data analysis

Neurons not classified as synchronized, non-synchronized, or mixed response, were only included in our analysis (as an atypical response) if they responded to acoustic pulse trains; the criteria for this was a significant vector strength for two neighboring IPIs and/or firing rate significantly above or below (2 o) the spontaneous rate for two neighboring IPIs.

Data analysis

The firing rate at an IPI of 3 ms divided by the maximum firing rate for all IPIs in the range of 35 ms and 75 ms.